ALBERT

Notes: The phenomenon of aerodynamic enrichment of heavy molecules seeded in supersonic free jets has been known since 1955. But its systematic exploitation in the generation of intensely focused molecular beams has been prevented by the lack of a quantitative and realistic explanation of the observed facts. Here, the aerodynamic focusing of CBr4, W(CO)6, and C2Cl6 molecules seeded in jets of He or H2 is studied experimentally, and found to be most singular under conditions similar to those known to produce sharply focused beams of microscopic spheres suspended in air jets. The gas mixture expands through thin-plate orifice into a vacuum chamber, forming a supersonic free jet. The spacial distribution of the heavy molecules in the jet is measured at varying distances L to the nozzle by scanning a thermocouple probe across a jet diameter. The probe is sufficiently small to interfere negligibly with the flow. The increment DV in the thermocouple voltage resulting from seeding the heavy gas on a given flow of He or H2 is seen to be a sensitive indicator of the local concentration of seed molecules in the jet. The following behavior is observed in terms of the same Stokes number or inertia parameter S that governs the simpler and better understood phenomenon of aerosol focusing. Below S=0.4 for H2 and S=0.2 for He, heavy molecule and aerosol beam widths are practically identical, and the boundary of the jet of heavy molecules is rather sharp. At higher values of S, aerosol beams show further reductionsin cross section, down to less than 10% of a nozzle throat diameter dn. In contrast, the measured heavy species minimal beam widths or waists at a distance L∼dn from the throat are around 0.5dn and 0.35 dn for jets of He and H2, respectively. In units of dn, these widths are several times larger than expected from elementary considerations on the defocusing effects due to Brownian motion (of the order of the square root of the molecular mass ratio between light and heavy molecules). Nonetheless, the thin-plate orifice nozzle yields considerably more concentrated jets of heavy gases than previously seen, with far-field enrichment factors for the seed species close to 50 in thecase of H2 jets. This technique, thus, appears to provide a greatly improved source for intense molecular beams. Aerodynamically focused beams have a sharp distribution of kinetic energies, being ideally suited for cross beam and beam surface studies. But they are not quite so optimal for spectroscopic studies because they require moderate source Reynolds numbers (of order 100), at which the heavy gas undergoes very little translational, rotational, or vibrational cooling.

Notes: New results concerning the mathematical properties of the Fokker–Planck equation describing the electron distribution function are presented. The validity of the approximations obtained by using a finite number of Legendre polynomials to describe the electron distribution function is discussed. It is shown that, due to the Landau form of the electron-ion collision operator, it is sufficient to use two or three Legendre polynomials in problems of interest. The theory is applied to the classical albedo problem as a test, and is also applied to determine the distribution and the heat flux in a heat front typical of laser plasma experiments. It is shown that the heat flux can be expressed as a sort of convolution of the Spitzer–Härm heat flux by a delocalization function. The convolution formula leads in a physically relevant way to the saturation and the delocalization of the heat flux.

Notes: The Boltzmann equations for a binary mixture of gases are considered in the asymptotic limit when their molecular weight ratio and the light gas Knudsen number are small quantities. A first mass-ratio expansion reduces the cross-collision operator of the light gas Boltzmann equation to a Lorentz form, uncoupling its kinetic behavior from that of the heavy gas. The light gas distribution function is then determined to first order in the Knudsen number, independently of the degree of nonequilibrium characterizing the heavy gas, whose influence is felt only through its hydrodynamic quantities. All transport coefficients arising are determined variationally for arbitrary interaction potentials using Sonine polynomial expansions as trial functions. A remarkable feature of this analysis is that it yields binary transport information (i.e., diffusion and thermal diffusion coefficients) from considering only the Boltzmann equation for the light gas. A second mass expansion reduces the cross-collision operator of the heavy gas equation to a Fokker–Planck form. The corresponding coefficients involve integrals over the light gas distribution function determined previously and are evaluated explicitly in terms of the hydrodynamic quantities and transport coefficients of the light gas. The heavy gas distribution function can be determined by solving a Fokker–Planck equation at dilutions large enough to make heavy–heavy collisions negligible, or by a new Knudsen number expansion when the molar fraction of the heavy gas is of order 1. In this latter case, the heavy gas kinetic behavior is independent of the light gas, being characterized by the same transport coefficients of the pure heavy gas. The problem is then reduced to a set of two-fluid hydrodynamic equations.

Notes: Particle acceleration in a localized electrostatic wave packet is studied. A weak field regime and a strong field regime are displayed. In the weak field limit a quasilinear relation for the velocity perturbation is derived. When the particles cross the accelerating field several times, a quasilinear equation for the distribution function is established. The theory is illustrated by numerical results from a model of resonance absorption of laser light by a plasma. Finally a model of electron reheating in resonance absorption including collisions is presented, leading to a nearly Maxwellian behavior for the hot component of the electron distribution function, f∼exp−(v/v0)8/3.

Notes: The electric field pattern is studied in the capacitor model of resonance absorption. Hydrodynamic and kinetic theory are used. The electric field is calculated for L(approximately-greater-than)10λD, where L is the density gradient length and λD the Debye length. The effect of collisional damping is studied. One obtains three different regimes. In the intermediate regime, the electric field amplitude is determined by the thermal convection, while the energy absorption is mainly caused by collisional damping.

Notes: The acceleration of electrons in a relativistic electron plasma wave is computed analytically and numerically. The electron acceleration is first computed as an expansion in powers of the electric field amplitude. A relation between the first- and second-order terms is derived, which corresponds to the relativistic Landau damping effect. Energy conservation in the wave frame enables one to obtain the maximum energy gain for a given injection energy. Optimum lengths are similarly calculated.